Floating Labels: Applying Dynamic Potential Fields forLabel Layout
Knut Hartmann, Kamran Ali, and Thomas Strothotte
Department of Simulation and GraphicsOtto-von-Guericke University of Magdeburg
Universitätsplatz 2, D-39106 Magdeburg, Germany{hartmann, kamran, tstr}@isg.cs.uni-magdeburg.de
Abstract. This paper introduces a new method to determine appealing place-ments of textual annotations for complex-shaped geometric models. It employsdynamic potential fields, which consider attractive and repulsive forces betweenpictorial elements and their textual labels. Several label candidates are computedand evaluated according to weighted penalty functions. The individual weightscan be adjusted according to global design decisions or user preferences. More-over, the user can re-arrange individual labels whereas the system re-adjusts theremaining labels. The method is demonstrated by the FLOATING LABEL system.
1 Introduction
A wide range of different application domains benefit from providing natural languageexplanations for pictorial elements. Frequently, they contain the denotation or unknowntechnical terms and are thus crucial to establish co-referential relations between picto-rial and textual expressions. The relation between pictorial elements and their associ-ated textual labels is indicated by meta-graphical objects such as connecting lines andanchor points placed on top of pictorial elements.
This concept is very attractive for interactive multi-modal information systems (e.g.,ZOOM ILLUSTRATOR [15], ILLUSTRATIVE SHADOWS [16]). In these systems two- orthree-dimensional geometric objects are associated with a set of labels. The contentto be presented within labels depends on the interaction context and therefore its sizechanges dynamically. An appealing label layout has to balance various optimal criteria,and should be adjustable to superior design decisions. This paper develops a new tech-nique to layout textual labels for complex-shaped geometric models, which balancesvarious evaluation criteria and is easily adjustable.
We collected a corpus of illustrations with many textual labels, extracted from anatomictextbooks, anatomic atlases, pictorial dictionaries, and technical documentations (e.g.,[7,17,5]). In a manual analysis we made some simple observations:
1. Labels should be placed near to their reference objects in order to prevent co-referential mismatches. They could be either placed within or outside their ref-erence objects (internal vs. external placement).
2. The length of the line connecting label and pictorial element should be minimized.3. The connecting line should be orthogonal to a main axis.
4. Crossings between connecting lines should be prevented.5. The placement of the anchor point should ease the identification of the pictorial
element.6. In dynamic environments the label placement has to be coherent, i.e., the label
position in timei +1 should be near to its position in timei.
The central idea to formalize these requirements is to establish positive and negativefields, which induce attractive and repulsive forces between pictorial elements and as-sociated labels. This strategy is known as theartificial potential field method. Section 2introduces this method. Section 3 formalizes the above observations in terms of attrac-tive and repulsive forces, which are also exploited to evaluate various label placementcandidates. Section 4 presents our initial results, and Section 5 discusses extensions.Finally, by analyzing related work in Section 6, Section 7 summarizes the new contri-butions of this work.
2 Potential Fields
Artificial potential fields have been introduced in Robotics by KHATIB [9] and becamepopular in other fields of Artificial Intelligence. They are inspired by attractive andrepulsive forces between electric particles. Therefore, the terms (electric) potential, andits first derivative, the (electric) field, are used.
The classical textbook on robot motion planning by LATOMBE [10] contains a popu-lar formalization, where attractors are modeled as global minima and retractors as max-ima within the potential field. The algorithm calculates attractive and repulsive forcesfor each possible positionp for a robot on a plane in a static environment. The attractiveforce steers the robot in the direction of the target:
Uattr(p) = c1ρ2goal (p)
whereρgoal (p) denotes the minimal distance fromp to the target andc1 is a scalingfactor. Moreover, for each obstacleBi a repulsive force is established:
UBi (p) =
{c2( 1ρi(p) −
1ρ0
)2 , ρi(p)≤ ρ00 , ρi(p) > ρ0
whereρi(p) denotes the minimal distance ofp to the obstacleBi , ρ0 the spatial influenceof the obstacle, andc2 is another scaling factor. The artificial potential field is definedas the sum of the attractive and all repulsive forces:
U(p) = Uattr +∑i
UBi
The algorithm determines the forces at the initial position of the robot and iterativelyredirects the robot according to the fieldF until it reaches a minimum within the poten-
tial field. Therefore, gradients−→∇ of the potential fieldU on the positionp are computed:
−→F =−
−→∇U(p)
Throughout this paper we will refer to the objects, which float according to these forcesasparticles. Real applications often employ grid-based space quantization. The chal-lenge in all these applications is to prevent those particles getting stuck within localminima without reaching the global minima.
3 The Floating Labels System
Some of the observations stated in Section 1 can be reformulated in terms of attrac-tive and repulsive forces. Figure 1 depicts several forces, which form the basis of ourFLOATING LABELS algorithm:
A: An attractive force between a pictorial element and its associated label,B: a repulsive force at the object boundary (i.e., the label should be placed entirely
within or outside its reference object),C: a repulsive force between the label and all other pictorial elements,D: repulsive forces between labels and the image boundary, andE: repulsive forces between labels.
Fig. 1. The force systemused by the FLOATINGLABELS algorithm. Thicklines denote pictorial el-ements, associated labelsand meta-graphical sym-bols (anchor points andconnecting line). Dashedlines indicate attractiveforces, and dotted linesshow repulsive forces.
Object j
Object i Label i
Label jAnchor
Point
Connecting Line
B
E
C
A
D
The formalization of potential fields in the previous section is based on the assump-tion of a single attractive force and constant repulsive forces. In contrast, the FLOAT-ING LABELS system induces a potential field for each individual geometric object andits associated label and assumes dynamic floating labels, inducing dynamic repulsiveforces. Note that the Forces A–D remain constant irrespective of the label configura-tion, whereas Force E is sensitive to the label configuration.
The static potential field, i.e., the accumulated attractive and repulsive Forces A–D, is used to determine a set of label placement candidates. Therefore, the algorithminserts some label particles in the potential field, which then move according to thefield F . To expand this point-feature label abstraction, the algorithm determines an areawhich contains the particle’s position and which minimizes the accumulated potential
over the label’s area. The FLOATING LABELS algorithm considers the label’s center andcorners. After estimating the best candidates, the overlappings between these labels areresolved in the second phase. In the following we will present the architecture of theFLOATING LABELS system and the formalization of the various attractive and repulsiveforces.
3.1 System Architecture
Figure 2 illustrates the architecture of the FLOATING LABELS system. In order to sup-port the integration of various applications, a domain expert establishes the connectionbetween geometric objects and terms in natural language. The domain expert containsor collects all information which is required to establish and exploit multi-modal co-referential relations. The FLOATING LABELS provides advices about an appealing labellayout.
Fig. 2. Architecture of FLOATINGLABEL system.
Phase 2
Phase 1
Domain Expert Initialization
Color-Code Rendering
Image Analysis
Static Force Field Calculation
Initial Label Placement
Label Competition
Dynamic Force Field Calculation
Decoration
The FLOATING LABELS algorithm is based on color-coded projections of the scenedisplayed in a 3D application. Therefore, a color-code renderer informs the domainexpert about the color encoding scheme, so that the color values could be used to deter-mine visible objects and to retrieve the label’s content.
The image analysis extracts the parameters required to compute the static poten-tial field. The initial label placement determines the start positions of label particles,
which then float to reach minima within the potential field. These point-feature labelabstractions are then expanded to area features and evaluated according to a number ofpenalty functions. The best label placement candidates are then re-adjusted accordingto the dynamic potential field. Finally, the label coordinates are sent to the applicationand rendered (decoration).1
3.2 Image Analysis
Based on color-coded projections, the image analyzer determines visible objects. Dueto occlusions, the projections of cohesive objects might be split into several segments.For each pictorial element the image analysis creates a list of all segments, their extent,size, and an internal point.
Determination of Internal Points: The placement of the anchor point is crucial to es-tablish the co-referential relation between a pictorial element and its label. Independentfrom the geometric properties of the reference object, an anchor point has to be placedwithin the pictorial element. For convex objects, the center of mass is a good candidate.However, the segments could have arbitrary shapes and may contain holes. Therefore,we use athinning algorithm [13], which iteratively shrinks the segment and stops as thesegment completely disappears. The last collapsed pixel is the most internal one andis selected as anchor point. This location is furthest away from the silhouette and liesinside the thickest region. This guarantees that the anchor point is placed at a visualdominant region. We will refer to this point within an objectO asinteria(O).
An analysis of the label layout of hand-made illustrations in our corpus reveals thatfrequently only one segment is labeled, i.e., only one pair of meta-graphical objects(anchor point, connecting line) establishes the co-referential relation between the picto-rial element and its associated label. Currently, the anchor point is placed on an internalpoint of the biggest visible segment. However, the results of our first experiments sug-gest to use the segment with the minimal distance to the textual label.
3.3 Static Force Field Calculation
For each object a separate potential field is constructed, considering the object’s area asan attractive field (Force A) and the area occupied by all other objects as repulsive force(Force C). Moreover, long-distance attractive forces ensure that each label is directedtowards the center of the largest segment of the reference object.
A Laplacian edge detector is applied on the color-coded image. A repulsive functionUsilh aims at placing the labels either within or outside their reference objects (Force B).Another repulsive functionUwall considers the minimal distance to the image borders, inorder to prevent labels from leaving the image (Force D). Both repulsive functions neednot to be recomputed for specific label configurations. In the following we will presentthe attractive and repulsive functions employed in the FLOATING LABELS system.
1 An extended version of this paper also includes the complete layout algorithm(http://wwwisg.cs.uni-magdeburg.de/ hartmann/Papers/floating-labels.pdf).
http://wwwisg.cs.uni-magdeburg.de/~hartmann/Papers/floating-labels.pdf
Fig. 3. A potential field for thetibia, a great bone located at thelower part of the knee joint. Redencodes attractive forces, andblue encodes repulsive forces.Black areas expose an equilib-rium between attractive and re-pulsive forces.
The attractive force between a pictorial element and its associated labels is defined by:
Uattr(p) =
{0 , p∈ area(O)c1
ρOη , p 6∈ area(O)
For each objectO which is projected onarea(O), ρO denotes the distance fromp tothe internal pointinteria(O) andη the maximal distance frominteria(O) to the imageboundary. This guarantees that the potential is within the interval[0,1]. The constantsci are some scaling factors. To prevent labels from overlapping the object’s silhouette,a repulsive forceUsilh is defined:
Usilh (p) =
{c2 , ρsilh ≤ ρS0 , ρsilh > ρS
whereρsilh denotes the minimal distance fromp to object boundary andρS is the sil-houette influence factor. Another repulsive force should prevent labels floating outsidethe image boundary:
Uwall (p) =
{c3(1− ρwallρW ) , ρwall ≤ ρW0 , ρwall > ρW
whereρwall denotes the minimal distance fromp to the image boundary andρW isthe boundary influence factor. Finally, the repulsive force of non-associated objects isconsidered by:
Urep(p) =
{c4 , p∈ area(Oi) ∧ Oi 6= O0 , else
The potential field for a given objectO is defined as the sum of the attractive and themaximal repulsive force:
U(p) = Uattr(p)+max(Uwall (p),Usilh (p),Urep(p))
Figure 3 depicts the potential field for the tibia, which is partly occluded by the liga-mentum patellae.
3.4 Initial Label Placement
After establishing the static potential field, label particles move from their start positionuntil they reach minima within the potential field. Currently, we experiment with a setof initial label positions: (a) the corners of projection, (b) the internal point of the largestobject segmentinteria(O), and (c) a point on the preferred main axis.Preferred Main Directions: Human illustrators prefer to connect label and anchorpoint with horizontal or vertical lines (Criterion 3). This observation guides the esti-mation of preferred label placements. Penalty values for four vectors starting from theanchor pointing to the main directions are computed. The penalty function considers:
– the number of non-reference objects which the connecting line crosses,– the length of segments, where the connecting line crosses non-reference objects,– the length of segments, where the connecting line crosses the reference object,– the amount of available free length to place the label and its distance from the
anchor point.
The penalty function aims at minimizing the number of non-referring pictorial elementscrossed by connecting lines and the distance between the anchor point and the label.Figure 4 presents the preferred main axis to connect reference object and label.
Fig. 4. Anchor points and preferred labeldirections.
3.5 Label Competition
While some of the label particles frequently reach identical local minima, there remaintypically 3 different candidate positions. These candidates are measured according to aset of evaluation criteria: theiraccumulated area potential Vpot , theirvisibility Vvis (areanot shared with other labels), thelength Vlen of the connecting line, and the minimalangle Vangle between the connecting line and either the horizontal or vertical axis. Dueto space restrictions we will only present the first evaluation criterion:
Vpot (L) = ∑p∈area(L)
U(p), L refers to the label under consideration
In order to compare these different measures, they are normalized into a standard range[0,1]. Therefore, for each pictorial element and each criterion the best and worst valuesof the label candidate set are determined.2 We found good results using a weighted sumof these measures, which enables us to consider global layout considerations. Figure 5-Left presents the label configuration after completing the first phase of the FLOATINGLABELS algorithm.
3.6 Dynamic Force Field Calculation
The evaluation criteria aim at an even label distribution over the available space. Dueto the ease of label replacement overlaps are not completely prohibited. A greedy re-adjustment algorithm is based on the assumption, that it is more easy to determinealternative appealing label positions for large objects than those for tiny objects.
Therefore, label overlaps are determined iteratively. One of these labels is selectedand pinned on its current position. The selection criteria consider the visible area andthe area of an axis-aligned bounding rectangle. Pinned label establishes repulsive forcesover an extended label area, which is added to the static potential fields of all objectsexcept it associated object. Then positions for the remaining unpinned labels are re-adjusted according to the corrected static potential fields (Force E). Figure 5-Rightpresents the final label configuration. The FLOATING LABELS system also enables theuser to apply manual corrections, while the system computes a balanced label configu-ration for the remaining labels.3
Fig. 5. Left: The initial label configuration for the knee joint. The model contains 19 dif-ferent objects. 15 are visible from the current point of view, and 14 of them are bigenough to place anchor points.Right: An improved label configuration. The greedyreposition algorithm was able to resolve both label overlappings.
2 Note that these measures are either absolute (visibility) or relative (accumulated area potential,line length and angle).
3 Not yet implemented.
3.7 Decoration
In this final step the meta-graphical objects (anchor points, connecting lines and labels)have to be integrated into an illustration in an aesthetic way. Therefore, we analyzed ourcorpus to extract appropriate render parameters for anchor points and connecting lines(e.g., shape, color). We found different rending styles:
Anchor Point Style: Some illustrators place them while others don’t.
Connecting Line Style:Illustrators use either dashed or solid lines. Solid lines seem tosegment the image into convex regions. In colored illustrations the choice of an appro-priate line color is very difficult. Most illustrators prefer black, but they frequently usewhite when the connecting line overlays large dark regions. Frequently the connectinglines are absent for short distances between anchor point and label. Turns in the con-necting line may also be used to prevent passing through dense, very detailed regionsor to prevent label overlaps.
In order to guarantee the visibility in all regions, the current implementation usessolid white line with black shadows for both anchor points and connecting lines.
3.8 Software
The FLOATING LABELS algorithm is based on 2D projections of 3D geometric mod-els from manually selected view points. Whenever hand-made illustrations of a similarobject were available, we adjusted these view points of the 3D models to match thesehand-made illustrations. Frequently, anatomic model are displayed from a set of differ-ent canonical viewing directions and thus several views of the same object are containedin our test set.
The 3D renderer is implemented in Open Inventor (Coin3D) and uses Qt to displaythe 2D image processing results. The basic algorithms are fully implemented, whereasthe code and optimizations for user interactions have to be finished until the time ofpresentation. The runtime to compute the label layout for complicated views was up to10 seconds on a modern PC.
4 Results
We tested our algorithm on more than 300 different geometric models taken from theViewPoint library and Princeton 3D model search engine. Most of the geometric modelsdo not separate individual objects. Even large 3D models with more than 100K verticesfrequently did not segment them at all. For high-quality models the number of individ-ual objects ranged between 10 and 25. The lack of highly segmented models was oneof the main obstacles during testing.
Figure 6 presents some label configurations computed by the FLOATING LABELSsystem. Our algorithm fulfills Criteria 1–3 and 5. According to Criterion 4, crossingsbetween connecting lines should be prevented as they are both distracting and mislead-ing, the Criterion 6 refers to dynamic environments. Both criteria are not yet consideredand subject to future work.
Within this limitation, we found the results quite promising. The label placementat local minima of potential field ensures an even label distribution. For illustrationswith few labels even the label placement according to preferred main axis achievedgood results. The consideration of repulsive force between labels in the second phaseimproves the label configuration on “hot spots”, i.e., regions where many labels have tobe arranged within small spatial areas. However, the most challenging example proves,that the static as well as the dynamic force field have to be fine-tuned and adjusted.
Fig. 6.Labels configurations automatically determined by the FLOATING LABELS sys-tem. For the heart model, the domain expert provided the denotation of geometric ele-ments, whereas for the other models the internal descriptions are displayed in the label.
5 Improvement / Future Work
Human illustrators employ a variety of decoration styles (see Section 3.7). Hence, addi-tional styles (e.g., labels without connecting lines, abbreviated label and legends) haveto be integrated into the FLOATING LABELS system.
The current algorithm did not consider intersections of connecting lines. Based uponour observation how humans prevent unwanted intersections, we developed a strategy
to resolve them. Whenever an intersection between two segments arises, the exchangeof their label positions eliminates this intersection. Because labels do not overlap, thisstrategy can also be applied to labels of different sizes. A recursive application is ableto resolve all intersections.
The main challenge is to integrate our force-field approach into an interactive 3D in-formation system. While our first experiments use full-scaled projections, the reductionof quantization would speed-up the calculation considerably. Therefore, further exper-iments will analyze the accuracy-efficiency tradeoff. Moreover, hot spots can be ob-served after the initial label configuration, which might reduce the number of differ-ent potential fields required to balance them. Finally, alternative strategies to resolveconflicts, could be applied on hot spot areas (remove labels, shrink label text, alterheight/width aspect of text boxes, legend creation . . . ).
We plan to exploit shape approximations with bounding objects (object-orientedbounding boxes, sphere trees) to compute the forces and gradients analytically. This willreduce the amount of space required to store pixel-based approximations of potentialfields and speed-up the calculation.
While the textual annotation or labels, as well as figure captions interrelate dis-tant pictorial and textual segments, text balloon in comics embed almost all textualinformation within illustrations. Cartoon-style illustrations are especially attractive, asour algorithm can be also applied to determine appealing layouts for complex-shapedballoons. Special repulsive functions aim at avoiding visually important regions, likehuman faces and hands. Moreover, the algorithm is suitable to determine very complexlayouts as required to design pictorial dictionaries. In all these application domains NPRshading techniques are most appropriate [18]. Hence, we will integrate our system intothe OPENNPAR renderer [8].
6 Related Work
The automatic design of well balanced layouts is a central aspect within computergraphics, computational geometry, and cartography. A variety of different techniqueshave been applied to generate complex layouts automatically: constraints [11], simu-lated annealing [6], or genetic algorithms [12]. The authors have chosen the potentialfield method primarily as the observations presented in Section 1 could be transformedin a simple and elegant way to a variety of attractive and repulsive forces.
We created test set of several high-quality 3D models, and comparable hand-madeillustrations, in order to extract human layout strategies and to evaluate our results. Inorder to compare different label layout techniques in terms of efficiency and visualbalanced results, the authors plan to apply them on this test set.
The potential field method was successfully applied to plan paths for real objectslike robots [10] as well as for virtual objects (e.g., camera planning in computer graph-ics). Several techniques were applied to prevent the object under control from gettingstuck into local minima. To guide the planning, BECKHAUS [1] introduced navigationobjects and dynamic potential fields. Our method has also to be compared with multi-agents path planning approaches in dynamic environments.
The appealing placement of labels is one of the central research subjects in car-tography. Here, point-feature abstraction of labels have been frequently used (see [4]).EBNER [6] exploited force fields for the label number maximation problem for pointfeatures. Their approach aims at placing the maximal number of axis-aligned labelscontaining their reference points without any overlapping. In order to find global min-ima they combined a gradient-based and a simulated annealing approach.
PREIM [15] pioneered the interactive exploration of complex spatial configurationsby visual and textual means. Textual annotation provides additional information abouttheir co-referential geometric objects. Their content depends on the interaction context,which requires dynamic changes in size. Therefore, the spatial configuration of labels isadjusted by applying a 2D distortion technique. Moreover, PREIM and RAAB [14] em-ployed mesh reduction to determine (multiple) anchor points for topographic complexgeometric objects in 3D. However, the labels in these interactive information systemsare either placed on special spatial area, placed manually or employ transparency toreduce the effect of occlusions.
BELL & FEINER [2] developed an algorithm to compute both covered and emptyregions in dynamic environments, which was successfully applied for a dynamic labellayout [3]. However, this algorithm is based on axis-aligned bounding boxes and doesnot yield best result for complex-shaped geometric object, whereas our algorithm workswithin the image space without such restrictions.
7 Conclusion
This paper introduces a label layout algorithm for complex-shaped geometric objects. Itworks on the image space without any approximation by bounding objects. Moreover,the label configuration is sensitive to global layout constraints, and can integrate usermanipulations and automatic adaptations. Even though the FLOATING LABELS systemis not yet integrated in an interactive 3D information system, our first experiments reveala great potential of improvement and enhancement to speed-up calculations.
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Floating Labels: Applying Dynamic Potential Fields for Label LayoutKnut Hartmann, Kamran Ali, Thomas Strothotte (University of Magdeburg)
